The Eta Pairing Revisited

F.  Hess; N. P.  Smart; F.  Vercauteren

Paper 2006/110

The Eta Pairing Revisited

F. Hess, N. P. Smart, and F. Vercauteren

Abstract

In this paper we simplify and extend the Eta pairing, originally discovered in the setting of supersingular curves by Baretto et al., to ordinary curves. Furthermore, we show that by swapping the arguments of the Eta pairing, one obtains a very efficient algorithm resulting in a speed-up of a factor of around six over the usual Tate pairing, in the case of curves which have large security parameters, complex multiplication by $D=-3$, and when the trace of Frobenius is chosen to be suitably small. Other, more minor savings are obtained for more general curves.

Note: Minor corrections and extra explanation included

Metadata

Available format(s): PDF PS
Category: Implementation
Publication info: Published elsewhere. Unknown where it was published
Contact author(s): nigel @ cs bris ac uk
History: 2006-06-16: last of 5 revisions; 2006-03-22: received; See all versions
Short URL: https://ia.cr/2006/110
License: CC BY

BibTeX

@misc{cryptoeprint:2006/110,
      author = {F.  Hess and N. P.  Smart and F.  Vercauteren},
      title = {The Eta Pairing Revisited},
      howpublished = {Cryptology {ePrint} Archive, Paper 2006/110},
      year = {2006},
      url = {https://eprint.iacr.org/2006/110}
}